This is a difficult question to answer, because the number keep growing.
Almost every year astronomers find new moons, using better telescopes on Earth and spacecraft flying through the solar systen. Some moons are so small that that their width is smaller than most cities on Earth.
The official list of moons in our solar system is kept by the International Astronomical Union, who are also in charge of naming them. Most of the names follow a theme.
For example, the moons of Jupiter are wives, girlfriends and daughters of the God Zeus, Saturn’s moons are named after ancient giants, and moons of Uranus are named after characters from Shakespeare’s plays.
As of September 2009 there are 151 moons orbiting planets and dwarf planets in our solar system.
- Mercury – 0
- Venus – 0
- Earth – 1
- Mars – 2
- Jupiter – 49
- Saturn – 53
- Uranus – 27
- Neptune – 13
- Pluto – 3
- Huamea – 2
- Eris – 1
You will find a full list of names at – http://planetarynames.wr.usgs.gov/append7.html